Question

Find the average Rate of Change for f(x) = 6x+6 over the interval [2,8] Simplify the answer.

Answer 1

6

Explanation:

We must evaluate the function at those points to know the values of f(x), like this:

`\begin{gathered} f(2)=6\cdot2+6=12+6=18 \\ f(8)=6\cdot8+6=48+6=54 \end{gathered}`

Knowing this, we can calculate the rate of change using the following formula:

`\begin{gathered} r=\frac{f(x_2)-f(x_1)_{}}{x_2-x_1} \\ \text{ replacing} \\ r=(54-18)/(8-2)=(36)/(6) \\ r=6 \end{gathered}`

The average Rate of Change is 6